# Lesson 5

Points, Segments, and Zigzags

- Let’s figure out when segments are congruent.

### Problem 1

Write a sequence of rigid motions to take figure \(ABC\) to figure \(DEF\).

### Problem 2

Prove the circle centered at \(A\) is congruent to the circle centered at \(C\).

### Problem 3

Which conjecture is possible to prove?

All quadrilaterals with at least one side length of 3 are congruent.

All rectangles with at least one side length of 3 are congruent.

All rhombuses with at least one side length of 3 are congruent.

All squares with at least one side length of 3 are congruent.

### Problem 4

Match each statement using only the information shown in the pairs of congruent triangles.

### Problem 5

Triangle \(HEF\) is the image of triangle \(HGF\) after a reflection across line \(FH\). Write a congruence statement for the 2 congruent triangles.

### Problem 6

Triangle \(ABC\) is congruent to triangle \(EDF\). So, Lin knows that there is a sequence of rigid motions that takes \(ABC\) to \(EDF\).

Select **all** true statements after the transformations:

Angle \(A\) coincides with angle \(F\).

Angle \(B\) coincides with angle \(D\).

Angle \(C\) coincides with angle \(E\).

Segment \(BA\) coincides with segment \(DE\).

Segment \(BC\) coincides with segment \(FE\).

### Problem 7

This design began from the construction of a regular hexagon. Is quadrilateral \(JKLO\) congruent to the other 2 quadrilaterals? Explain how you know.